The use of in-line spectrophotometers in printing systems is increasing. Depending upon the mode of operation, a spectrophotometer will report L*a*b* values, spectral reflectance values at some sampling frequency, and other measurements, such as density. For example, a spectrophotometer typically provides spectral information comprising a representative signal of the printed colors of the image and preferably also provides L*, a*, b* values, XYZ, etc. values depending on the desired color description. One such spectrophotometer may be that disclosed in U.S. Pat. No. 6,384,918 by Hubble, III et al. for a SPECTROPHOTOMETER FOR COLOR PRINTER COLOR CONTROL WITH DISPLACEMENT INSENSITIVE OPTICS, the disclosure of which is hereby incorporated by reference. The spectrophotometer is for non-contact measurement of colored target areas such as test patches on moving printed test sheets in an output path of a color printer, where test patches may be sequentially angularly illuminated with multiple different colors, and a photosensor providing electrical signals in response. The spectrophotometer includes a lens system for transmitting that reflected illumination (multiple illumination sources comprise approximately eight or more individual LEDs) from the test patch. The exemplary spectrophotometer provides non-contact color measurements of moving color targets variably displaced therefrom within normal paper-path baffle spacings.
Customers expect that absolute color accuracy will be improved through the use of these devices, although several factors will conspire to reduce accuracy. These features include cycle-up to cycle-up variability (change in the printer's response between calibration and use); page-to-page variability, and instrument error. Instrument error can be further divided into consistent error and random variation. Random variation cannot be avoided, but can be reduced by averaging. But, instrument error can be reduced by calibrating the spectrophotometer, in particular as described in connection with the presently described embodiments of this application.
It is well known that spectrophotometers have instrument-to-instrument differences, resulting in different responses between instruments reading the same patches printed on the same prints. The solution in the past has been to use a single instrument whenever making comparisons, and to use a single device to measure prints from both engines in a multi-engine color system. A limitation this presents is in a shop or system with multiple engines, each equipped with their own in-line spectrophotometer, the intra-instrument variability is one limiting factor for engine to engine match, unless pages are manually carried to a single instrument. There is, therefore, a need for improved methods of reducing the inter-instrument difference between spectrophotometers.
In this regard, a paper by Roy Berns (R. S. Berns and K. H. Petersen, “Empirical Modeling of Systematic Spectrophotometric Errors”, Color Research and Application, 13, (4), 243, (1988), which is incorporated herein in its entirety by reference) describes a method of making spectrophotometers match better (in spectral space); another paper by Danny Rich (D. Rich and D. Martin, “Improved model for improving inter-instrument agreement of spectrocolorimeters”, Analytical Chemica Acta, 380, 263-276, (1999), which is incorporated herein in its entirety by reference, describes an improvement on that method. This method is quoted and used in yet another paper by Rich (D. Rich Graphic technology—Improving the inter-instrument agreement of spectrocolorimeters Committee for Graphic Arts Technologies Standards White Paper, Reston, Va. January 2004), which is incorporated herein in its entirety by reference and describes using the method to improve the match of a set of spectrophotometers. The match was generally improved from a mean of 0.447 to 0.191; 75th percentile 0.290 to 0.090 and a maximum (over 420 samples) of 1.32 to 1.190.
The model used in both Rich articles is as follows:
            R      o        ⁡          (      λ      )        =            β      0        +                  β        1            ·                        R          t                ⁡                  (          λ          )                      +                  β        2            ·                        ⅆ                                    R              t                        ⁡                          (              λ              )                                                ⅆ          λ                      +                  β        3            ·                                    ⅆ            2                    ⁢                                    R              t                        ⁡                          (              λ              )                                                ⅆ                      λ            2                              
The four beta values are separately optimized for each wavelength. The first represents an offset, the second a scale, the third a linear difference in wavelength scale (referring to a linear error in position of the wavelength samples), and the fourth a bandwidth correction.
Mohammadi and Berns, Diagnosing and Correcting Systematic Errors in Spectral-Based Digital Imaging, 13th Color Imaging Conference Final Program and Proceedings (Scottsdale, Ariz.), Society for Imaging Science and Technology & Society for Information Display (November 2005), which is incorporated herein in its entirety by reference, went further, adding quadratic terms for both scale and wavelength scale, and a sinusoidal wavelength scale term. The quadratic and sinusoidal wavelength scale were least frequently significant in the regressions (one regression per wavelength).
In all of these methods, three point numerical first and second derivative formulas are used, which means that the adjustments to the input reflectances are entirely dependent on the reflectances themselves, and the two adjacent reflectances.